In known drawheads of this kind the fallers used for drawing the woolen fleece or the like, which have a plurality of needles, are disposed on rotating drums, wherein the needles move in a circle. Attempts have also been made to move the fallers along the work area over a longer segment in a straight line through the material to be drawn, wherein propulsion of the fallers was made by means of gear chains. However, such gear chain drives have the basic disadvantage of being mechanically unreliable and of being very noisy.